2011 Fiscal Year Final Research Report
A study on the dimension of global sections of adjoint bundles of polarized manifolds by the sectional geometric genus
| Project/Area Number |
20540045
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kochi University |
|---|
Principal Investigator |
FUKUMA Yoshiaki 高知大学, 教育研究部・自然科学系, 教授 (20301319)
|
|---|
| Project Period (FY) |
2008 – 2011
|
| Keywords | 偏極多様体 / 豊富な因子 / 随伴束 / 断面幾何種数 |
|---|
| Research Abstract |
Let X be a smooth projective variety of dimension n over the field of complex numbers and let L be an ample line bundle on X. Then we call this pair(X, L) a polarized manifold. In this investigation, we studied an integer m which satisfies the following property : for any 4-dimensional polarized manifolds(X, L) whose adjoint bundle K_X+ L is nef, m(K_X+ L) has a global section. We proved that if m is greater than or equal to 3, then m(K_X+ L) has a global section. Furthermore we proved that we can apply this method to the case where n is less than or equal to 11. We also studied some invariants of polarized manifolds. These results will be useful for the study of the dimension of global sections of adjoint bundles.
|
